Problem Description

Novel applications for biocompatible, magnetic micro- and
nanoparticles are being developed which include magnetically targeted
drug and gene delivery. In these systems, therapeutic drugs or genes
are attached to functionalized magnetic particles and injected near
the target site. External magnetic fields of varying characteristics
(usually produced by rare earth magnets) are applied to the site
externally in order to concentrate the particles at the target. In the
case of gene delivery, it is envisaged that this method will achieve
higher transfection and hence expression rates. In the case of drug
delivery, therapeutic drugs are concentrated at the site in the body
where they are needed.

At present, there are several types of particles commercially
available. These particles vary in size, magnetic properties and
chemical composition (though the primary magnetic component of the
particles is generally magnetite - Fe3O4). For
the vast majority of these particles, the magnetic component exists in
a superparamagnetic state. In this case, the force exerted on the
particle is a translational force directed along the applied field
vector and is dependent on the magnetic properties of the particle and
the surrounding medium, the size and shape of the particles and the
product of the magnetic flux density and the field gradient.

As different sites and applications have different requirements for
these systems (for example, the distance to the magnet or the velocity
of the flowing particles will vary) we would like to generate either a
family of curves, a chart or a computer program which will enable us
to choose the appropriate field strength and geometry for a particular
application based on the known flow, physical properties of the
particles and distance from the magnetic field source to the
target.

We are also developing magnetically "blocked" particles to be used
in these applications. These particles will experience a torque when
the particle's magnetization vector is at an angle to the applied
field. We propose to vibrate these particles by oscillating the
magnetic field and would like to determine optimum vibrational
frequencies based on a theoretical examination of viscous damping
under physiologically relevant conditions. Applications and problems
in magnetic hyperthermia will also be discussed.

Study Group Report

A general three-dimensional model was formulated, involving
external magnetic forces and strokes drag, but neglecting
inter-particle interactions and Brownian motion. To solve for
particular situations the magnet geometry must be simple enough to
allow explicit calculation of the magnetic field, hence we then
considered a simple two-dimensional scenario in which the magnet was a
finite one-dimensional plate, generating a two-dimensional field, and
was placed parallel to the blood vessel, which was represented by a
two-dimensional channel.

For this set-up, trajectories of the magnetic particles may be
computed quite easily, and particle `capture' investigated. Roughly
speaking, the crucial factor is (not surprisingly) found to be the
separation between the channel and the magnet. For sufficiently large
separations no particles can be captured and held by the magnetic
field. For moderate separations a certain proportion of particles are
captured, and accumulate in a single equilibrium spot on the vessel
wall. For yet smaller separations, a greater proportion of particles
are captured; and there are two possible equilibrium capture positions
where particles accumulate on the vessel wall. These results are in
qualitative agreement with simple in vitro experiments of the process,
with similar geometry.

Many points of practical importance remain to be addressed,
including particle–particle interactions (both magnetic and
hydrodynamic); Brownian motion, and geometrical effects (both of the
vessel and its walls, and the particles). In addition, although the
particles have been shown to accumulate on the vessel wall in our
simple model, what is important in practice is whether they become
embedded, so that they remain in situ when the magnetic field has been
removed. Further work is required to address all these issues
satisfactorily.